Class 12 Exam  >  Class 12 Notes  >  Sample Papers for Class 12 Medical and Non-Medical  >  Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4

Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical PDF Download

Class-XII


Time: 120 Minutes


Max. Marks: 40

General Instructions :

  1. This question paper contains three sections A, B and C. Each part is compulsory.
  2. Section - A has 6 short answer type (SA1) questions of 2 marks each.
  3. Section - B has 4 short answer type (SA2) questions of 3 marks each.
  4. Section - C has 4 long answer type questions (LA) of 4 marks each.
  5. There is an internal choice in some of the questions.
  6. Q14 is a case-based problem having 2 sub parts of 2 marks each.

Section - A

Q.1. Evaluate Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
OR
Find: Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical.

Let I = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
I = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Let cos x + sin x = t
⇒ (cosx - sinx)dx = dt
⇒ I = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= log|t| + C
= log|cosx + sinx| + C
OR
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
f(x) = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical


Q.2. Find the sum of the order and the degree of the following differential equations: 

Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical

Here,
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical 
Thus, order is 2 and degree is 3. So, the sum is 5.


Q.3. Find the position vector of a point which divides the join of points with position vectors Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical and Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical externally in the ratio 2 : 1.

Required vector = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical


Q.4. Find the equation of line passing through (1, 1, 2) and (2, 3, –1).

Equation of line passes to (x1, y1, z1) and (x2, y2, z2)
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
So, Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical

Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical


Q.5. If A and B are two independent events, then prove that the probability of occurrence of at least one of A and B is given by 1 – P(A’) · P(B’).

Required probability
= P(A ∩ B)
= P(A) + P(B) – P(A) · P(B)
= P(A) [1 – P(B)] + 1 – P(B’)
= P(A) P(B’) – P(B’) + 1
= [1 – P(B’)] [1 – P(A)]
= 1 – P(A’) P(B’) (Hence Proved)


Q.6. One bag contains 3 red and 5 black balls. Another bag contains 6 red and 4 black balls. A ball is transferred from first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is red.

P (Red transferred and red drawn or black transferred and red drawn)
= 3/8 x 7/11 + 5/8 x 6/11
= 51/88

Section - B

Q.7. Find : Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical.

Let
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
⇒ x + 1 = (Ax + B)x + C(x2 + 1) (Anidentity)
Equating the coefficients, we get
B = 1, C = 1, A + C = 0
Hence, A  = –1, B = 1, C = 1
The given integral
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical + log|x| + c


Q.8. Find the general solution of the following differential equation:
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
OR
Find the particular solution of the following differential equation, given that y = 0 when x = π/4: Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical

We have the differential equation
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
The equation is a homogeneous differential equation.
Putting y = vx
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
The differential equation becomes
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
⇒ cos v dv = -dx/x
Integrating both sides, we get
log|cosec v - cotv|= -log |x|+ logK,
K > 0 (Here, log K is an arbitrary constant.)
⇒ log|(cosec v - cotv)x| =  logK

⇒ |(cosec v - cotv)x| = K
⇒ (cosec v - cot v)x = ± K
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
which is the required general solution.
OR
The differential equation is a linear differential equation
⇒ IF = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical = sin x
The general solution is given by

ysin x = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical

⇒ ysin x =Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
⇒ ysin x = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
⇒ ysin x =  Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
⇒ ysin x =  Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
⇒ ysin x =Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Given that y = 0, where x = π/4,
Hence, 0 = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
⇒ c = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Hence, the particular solution is

y = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical- Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Alternative method
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
The differential equation is a linear differential equations
∴ I.F. = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical=  sin x
The general solution is given by
ysin x = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
ysin x = 2x - Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
ysin x = 2x - Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
ysin x = 2x - 2 tanx + 2secx + c
Given that
y = 0 when x = π/4
0 = π/2 - 2 + √2 + C
C = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Since, the particular solution is
ysin x = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical


Q.9. If Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical, then show that Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical.

We have
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Also, Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical cannot be both perpendicular to Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical and parallel to Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Hence, Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical.


Q.10. Find the shortest distance between the following lines:

Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
OR
Find the vector and the cartesian equations of the plane containing the point Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical and parallel to the lines Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical and Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical = 0

Here, the lines are parallel. The shortest distance
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Hence, the required shortest distance
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical units
OR
Since, the plane is parallel to the given lines, the cross product of the vectorClass 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical and 

Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical will be a normal to the plane
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
The vector equation of the plane is
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
or, Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical = 2
and the cartesian equation of the plane is
x -z- 2 = 0.

Section - C

Q.11. Find: Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical

Let,
I = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
(On dividing Nr and Dr. by cos3 x)
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical 
On substituting tan x = t  and sec2x dx = dt,
We get
I = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical+ Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical+ Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical + Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical+Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical+ Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical


Q.12. Find the area of the region bounded by the curve x= 4y and the straight-line x = 4y– 2
OR
Area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x2+ y2 = 32 

As x2 = 4y and x = 4y – 2
So, x2 = x + 2
x2 - x - 2 = 0
(x -2)(x + 1) = 0
x = -1, 2
For x=−1,     y = 1/4  and for x = 2, y = 1
Points of intersection are (-1, 1/4) and (2, 1)
Graphs of parabola x2 = 4y  and x = 4y  2    are     shown in the following figure:
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
A= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= 9/8 sq. units
= 1 x 1/8 sq. units
OR
We have y = 0, y = x and the circle x2 + y= 32 in the first quadrant.
Solving y  = x with the circle
x+ x2 = 32
x2 = 16
x = 4 (In the first quadrant)
When x  = 4, y = 4 for the point of intersection of the circle with the x-axis.
Put y  = 0 in circle
x+ 0 = 32
x = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
So, the circle intersects the x-axis at Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical

Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
From the above figure, area of the shaded region,
A = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical+ Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= 8 + [8π - 8 - 4π]
= 4π sq. units


Q.13. Find the shortest distance between the lines Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical and 

Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical. If the lines intersect find their point of intersection.

We have
a1 =Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
b1 = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
a2 = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
b2 = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical

Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical+ Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical = 16 - 16 = 0
∴ The lines are intersecting and the shortest distance between the lines is 0.
Now for point of intersection
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical = Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
⇒ 3 + λ = 5 + 3μ ....(i)
2 + 2λ = -2 + 2μ ....(ii)
-4 + 2λ = 6μ
Solving (i) and (ii) we get μ = –2 and λ= –4 Substituting in equation of line we get
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Point of intersection is (–1, –6, 12)

Case-Based/Data Based

Q.14. Board exam are near by, so Mr. Sharma decided to check the preparation of the few weak students in the class. He chooses four students A, B, C and D then a problem in mathematics is given to those four students A, B, C, D. Their chances of solving the problem, respectively, are 1/3,  1/4, 1/5 and 2/3. Based on the given information answer the following questions. What is the probability that:
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical 
(i)   the problem will be solved?
(ii) at most one of them solve the problem?

Let
E be the event = A solves the problem
F be the event = B solves the problem
G be the event = C solves the problem
H be the event = D solves the problem
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
(i) The required probability
= P(E ∪F∪G∪ H)
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= 1 - 2/3 x 3/4 x 4/5 x 1/3
= 13/15
(ii) The required probability
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical
= 7/15 + 1/30 + 2/45
= 42 + 3 + 4/90
= 49/90

The document Class 12 Mathematics: CBSE Sample Question Paper- Term II (2021-22)- 4 | Sample Papers for Class 12 Medical and Non-Medical is a part of the Class 12 Course Sample Papers for Class 12 Medical and Non-Medical.
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